On Sequences of Bounded Variation


  • Kanka Dey STIC


sequence of bv, boundedness, convergence, monotonicity


In this article, the sequence of bounded variation was considered and its various properties, with examples and counterexamples, were studied in detail. Also, the study focused on the relationship of the sequence of bounded variation with monotonic sequences, convergent and divergent sequences. Further, some necessary and sufficient conditions and sometimes only necessary condition was studied, where sufficient condition is not always true, with examples. The space of the sequence of bounded variation also considered, which is denoted by bv. Here it is shown that bv is closed with respect to addition and multiplication. Hence with respect to some norm bv is a Banach space. Many studies are being found in history regarding the summability of sequence of bounded variation with respect to different types of infinite matrices. Here the summability properties of the sequence of bounded variation were not considered.


Iyer, V.G. (1977). Mathematical Analysis. New Delhi: Tata Mc GrawHill Publishing Company Ltd.

KiriƟci, M. (2014). The sequence space bv and some applications. arXiv preprint arXiv:1403.1720. Retrieved from: https://arxiv.org/pdf/1403.1720.pdf

Kirisci, M. (2016). The Application Domain of Infinite Matrices on Classical Sequence Spaces. arXiv preprint arXiv:1611.06138. Retrieved from: https://arxiv.org/pdf/1611.06138.pdf

Lahiri, B.K. (1996). Elements of Functional Analysis. Calcutta: The World Press Private Limited.

Loya, P. (2006). Amazing and Aesthetic Aspects of Analysis: On the incredible infinite. UTM series of Springer Verlag.